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The Rate of Convergence for Subexponential Distributions and Densities
Lithuanian Mathematical Journal, 2002This paper builds on the previous literature and extends the results presented there, especially those of the authors [Lith. Math. J. 38, 1-14 (1998) and Liet. Mat. Rink 38, No.~1, 1-18 (1998; Zbl 0935.60005)]. A distribution function \(F\) on \([0,+\infty[\) is called subexponential if \(\lim_{x\to+\infty} (1-F^{*n}(x))/(1-F(x))=n\) for all \(n\geq 2\)
Baltrūnas, A., Omey, E.
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On the Constant in the Definition of Subexponential Distributions
Theory of Probability & Its Applications, 2000A distribution \(G\) on \([0, +\infty)\) is said to be subexponential if it does not have a compact support, if for every \(y > 0\), \(\lim_{x \to +\infty} G([x+y, +\infty))/G([x, +\infty)) = 1\), and if \(\lim_{x \to +\infty} G*G([x, +\infty))/G([x, +\infty)) = c\) for some constant \(c\). Those distributions were introduced by \textit{V.
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Subexponential distributions and characterizations of related classes
Probability Theory and Related Fields, 1989Let S(\(\gamma)\), \(\gamma\geq 0\), denote the class of distributions F satisfying \[ (i)\quad \lim_{x\to \infty}\bar F^{2*}(x)/\bar F(x)=2\int^{\infty}_{0}e^{\gamma Y}dF(y)0\), are characterized by means of subexponential densities. As an application we derive a result on the asymptotic behaviour of densities of random sums.
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The structure of the class of subexponential distributions
Probability Theory and Related Fields, 1988Let \(X_ 1,X_ 2,...,X_ n\) be a sequence of positive, independent, identically distributed random variables with the same distribution function (d.f.) F and denote by \(X_{1:n}\leq X_{2:n}\leq...\leq X_{n:n}\) the order statistics of the sample. We characterize the class of d.f.
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Siberian Mathematical Journal, 2002
The author studies the properties of subexponential distributions and finds new sufficient and necessary conditions for the membership in the class of these distributions. He establishes a connection between the classes of subexponential and semiexponential distributions and gives conditions for preservation of the asymptotics of subexponential ...
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The author studies the properties of subexponential distributions and finds new sufficient and necessary conditions for the membership in the class of these distributions. He establishes a connection between the classes of subexponential and semiexponential distributions and gives conditions for preservation of the asymptotics of subexponential ...
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Subexponential distribution functions and some applications
Advances in Applied Probability, 1979Paul Embrechts +2 more
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The Subexponential Class of Probability Distributions
Theory of Probability & Its Applications, 1975openaire +1 more source